We emphasize that smallness of the initial data is only required in a weaker norm than the one of \(X^{\textup {W}}_0\) . The other smallness constraints in Theorem REF  can be achieved by making either \(\Vert (p_0,p_1)\Vert _{X^{\textup {W}}_0}\)  small or final time \(T\)  short enough. This theoretical framework thus agrees well with ultrasonic applications, where typically the final time will be short and the data smooth, but not necessarily small; see, for example, [1]} and [2]}.
